ModelBuilder - "iterate rasters" doesn't exclude files outside extent

I've received a data request and need to use a polygon on a directory tree to extract data within a specified polygon (shp format).

I created a model using "iterate rasters" (using the recursive option) and "extract by mask"
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The model runs, but for some reason, doesn't ignore rasters outside of the polygon extent. Instead, it processes all of the rasters. Outputs for rasters within the polygon are the actual values (as intended). Outputs for rasters located outside the polygon recalculated to "no data". This takes a hugely unnecessary amount of time.

The polygon file is specified for both "extents" and "raster analysis > mask" in the environments in addition to being specified as an input for the "extract by mask" tool itself.

Any suggestions for settings (or a different approach) to force Arc to ignore rasters outside my analysis area (or otherwise accomplish task efficiently) would be much appreciated.

Thanks,
Will

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